Bechoros 35b - cohanim suspected on mumei bechor

The gemara on 35b (and in many other places) says that cohanim are suspected about mumim on their bechors. Someone else needs to testify that the animal got the mum itself. Yisroelim are not chashudim, and so it is brought in Yoreh Deah (314, 321).
I would have thought this is because the Cohen benefits from the bechor, not the Yisroel. However, this din seems to be true for a safek bechor as well, even though the Yisroel is going to get to keep it, and so it is brought in the Shulkhan Arukh. Why is this?

One pair of answers is given by the P'rishah, Yoreh Deah 314(14). His second answer is simpler: since the case of the Yisroel is only a safek bechor, there is never more than a safek issur, so Chazal did not need to enforce their suspicion.

His first answer is interesting: We don't actually suspect a Cohen (or a Yisroel) of being willing to violate the Torah (the issur of intentionally making a mum on a korban) just for the benefit of eating it. The real reason the Cohen is suspected is that he is stuck taking care of the animal indefinitely, unless it gets a mum. It's that unbounded obligation that causes the suspicion.
So for our case of safek bechor, that reason doesn't apply. If the Yisroel ever gets too frustrated with waiting, he can just give the animal to a Cohen (and the Shulkhan Arukh poskins that the Cohen has to take it).

This reminds me of another issue: the question of whether a bechor is a positive or a negative - see the question I asked elsewhere (https://gemaraboards.forumotion.com/t116-bechor-positive-or-negative). Does this answer only make sense if a bechor is a net negative? Or might the owner get desperate anyhow, when it happens that this bechor turns out to be bulletproof for years?

Update 1/21/2017: I have a few other problems with the Prishah's first answer.
1) He rejects that the owner would intentionally make a mum just to be able to eat it. But that seems to be an accepted point of view in the gemara, where a "Ro'eh Cohen" might be a Yisroel shepherd working for a Cohen, hoping to get part of the feast when the bechor is slaughtered. Or a Cohen shepherd working for a Yisroel, who hopes to be given the animal as the designated Cohen when it gets its mum.
2) He is going with his shitah that the Cohen is required to accept the animal from a Yisroel, even if it is a safek bechor. The Rema says that too, I guess that's the halacha, but the poskim bring that other kadmonim (Terumas Hadeshen and others) disagree. If the Cohen doesn't need to accept it, the Yisroel can be desperate on the case of safek bechor as well.
3) If it is allowed to be machnis l'kipah, as some Rishonim hold (but not the Shulchan Aruch), a Cohen wouldn't get desperate either.

I see there's a Tosefos on Temurah 8b (d"h dilma) that seems to reject the Perisha's second answer. That is, they bring the case of a Yisroel's safek bechor as a kashya, thereby proving that Chazal considered a Yisroel more reliable than a Cohen even where he has something to gain.
They don't explain the difference between Yisroel and Cohen, but they do say that the gemara's case there is an exception: Chazal didn't want a Cohen to sell his (un)blemished animal to a Yisroel. Tosefos explains that there the Yisroel owner will be tempted to make a mum and say it happened by the previous owner, something that isn't possible where it was born by him. In that case they say that he would be afraid - אז ירא להטיל בו מום מאחר שנולד ברשותו דאין לו להשמט בשום דבר - since he has no wiggle room.
I'm wondering if this could be their explanation why a Cohen is suspected: since he normally gets his animal from a Yisroel he might be tempted to say it had a mum. Doesn't seem like that would cover all cases, though. Could they have said, לא פלוג - this is why there's a general ne'emanus on a Yisroel, and not on a Cohen? That anyhow seems to be what they are saying in the ה"א of the gemara in Temurah according to Tosefos: We've found a case where the Yisroel is suspected, but we don't say that he isn't ne'eman to tell us that a mum happened by accident; we keep the general rule that a Yisroel is ne'eman, and solve the problem in a different way by not letting the Cohen sell him the bechor.

-Update 1/21/2017 I got to ask Rav Tzvi Berkowitz shlit"a about this Tosefos and he drew roughly the same conclusion I did, boruch shekivanti.

Writeup of this issue: https://drive.google.com/open?id=0B1_EiCPi0cabZF9SeUhxb1hNRWc